Abstract: In the vibration analysis of beam bending problems, none of existing mass lumping schemes that are mathematically rigorous (ignored mass of rotational degree of freedom) are available to maintain the lumped mass matrix symmetric and positive definite up to now, which leads to the difficulty in generating symmetric and positive definite matrix. It has caused great inconvenience to analyses in both the time and frequency domain. Within the framework of the partition of unity (PU), the PU functions and local approximations on the patches are retrieved from Hermitian interpolations via numerical manifold method. Next, the variation principle is integrated using the definition of integral of a scalar function on a manifold to retrieve the diagonal block mass matrix. In addition, compared with consistent mass matrix, our method could achieve higher precision and speed, especially for higher order modes.

Key words: finite element method, beam vibration analysis, mass lumping, numerical manifold method, partition of unity